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Symplectic Quantum Mechanics and Chern-Simons Gauge Theory I  [PDF]
Lisa C. Jeffrey
Mathematics , 2012, DOI: 10.1063/1.4804152
Abstract: In this article we describe the relation between the Chern-Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these two Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional.
Chern-Simons Reduction and non-Abelian Fluid Mechanics  [PDF]
R. Jackiw,V. P. Nair,So-Young Pi
Physics , 2000, DOI: 10.1103/PhysRevD.62.085018
Abstract: We propose a non-Abelian generalization of the Clebsch parameterization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parameterization allows a canonical description of conventional fluid mechanics.
Symplectic structure free Chern-Simons Theory  [PDF]
Won Tae Kim,Yong-Wan Kim,Young-Jai Park
Physics , 1998, DOI: 10.1088/0305-4470/32/12/017
Abstract: The second class constraints algebra of the abelian Chern-Simons theory is rigorously studied in terms of the Hamiltonian embedding in order to obtain the first class constraint system. The symplectic structure of fields due to the second class constraints disappears in the resulting system. Then we obtain a new type of Chern-Simons action which has an infinite set of the irreducible first class constraints and exhibits new extended local gauge symmetries implemented by these first class constraints.
Symplectic Reduction and Symmetry Algebra in Boundary Chern-Simons theory  [PDF]
Phillial Oh,Mu-In Park
Physics , 1998, DOI: 10.1142/S0217732399000274
Abstract: We derive the Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary by using the symplectic reduction method and the Noether procedures.
On Statistical Mechanics of Non-Abelian Chern-Simons Particles  [PDF]
Taejin Lee
Physics , 1996,
Abstract: Lee replies to the comment on "Statistical Mechanics of Non-Abelian Chern-Simons Particles" by C. R. Hagen
Symplectic Quantization of the CP$^1$ Model with the Chern-Simons Term  [PDF]
Yong-Wan Kim,Young-Jai Park,Yongduk Kim
Physics , 1995,
Abstract: The symplectic formalism is fully employed to study the gauge-invariant CP$^1$ model with the Chern-Simons term. We consistently accommodate the CP$^1$ constraint at the Lagrangian level according to this formalism.
Statistical Mechanics of Non-Abelian Chern-Simons Particles  [PDF]
Taejin Lee
Physics , 1995, DOI: 10.1103/PhysRevLett.74.4967
Abstract: We discuss the statistical mechanics of a two-dimensional gas of non-Abelian Chern-Simons particles which obey the non-Abelian braid statistics. The second virial coefficient is evaluated in the framework of the non-Abelian Chern-Simons quantum mechanics.
Symplectic structure of N=1 supergravity with anomalies and Chern-Simons terms
De Rydt, Jan;Rosseel, Jan;Schmidt, Torsten T.;Van Proeyen, Antoine;Zagermann, Marco
High Energy Physics - Phenomenology , 2007, DOI: 10.1088/0264-9381/24/20/017
Abstract: The general actions of matter-coupled N=1 supergravity have Peccei-Quinn terms that may violate gauge and supersymmetry invariance. In addition, N=1 supergravity with vector multiplets may also contain generalized Chern-Simons terms. These have often been neglected in the literature despite their importance for gauge and supersymmetry invariance. We clarify the interplay of Peccei-Quinn terms, generalized Chern-Simons terms and quantum anomalies in the context of N=1 supergravity and exhibit conditions that have to be satisfied for their mutual consistency. This extension of the previously known N=1 matter-coupled supergravity actions follows naturally from the embedding of the gauge group into the group of symplectic duality transformations. Our results regarding this extension provide the supersymmetric framework for studies of string compactifications with axionic shift symmetries, generalized Chern-Simons terms and quantum anomalies.
An Extended Abelian Chern-Simons Model and the Symplectic Projector Method  [PDF]
L. R. U. Manssur,A. L. M. A. Nogueira,M. A. Santos
Physics , 2000, DOI: 10.1142/S0217751X02010625
Abstract: The Symplectic Projector Method is applied to discuss quantisation aspects of an extended Abelian model with a pair of gauge potentials coupled by means of a mixed Chern-Simons term. We focuss on a field content that spans an N=2-D=3 supersymmetric theory whenever scalar and fermionic matter is suitably coupled to the family of gauge potentials.
Non-Abelian Chern-Simons Quantum Mechanics  [PDF]
Taejin Lee,Phillial Oh
Physics , 1993, DOI: 10.1103/PhysRevLett.72.1141
Abstract: We propose a classical model for the non-Abelian Chern-Simons theory coupled to $N$ point-like sources and quantize the system using the BRST technique. The resulting quantum mechanics provides a unified framework for fractional spin, braid statistics and Knizhnik-Zamolodchikov equation.
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